For many kinds of business and scientific applications, the ability to generate accurate forecasts of future values of various measures (e.g., retail sales, or demands for various types of goods and products) based on previously collected data is a critical requirement. The previously collected data often consists of a sequence of observations called a “time series” or a “time series data set” obtained at respective points in time, with values of the same collection of one or more variables obtained for each point in time (such as the per-day sales for a particular inventory item over a number of months, which may be recorded at an Internet-based retailer). Time series data sets are used in a variety of application domains, including for example weather forecasting, finance, econometrics, medicine, control engineering, astronomy and the like.
The statistical properties of some time series data, such as the demand data for products or items that may not necessarily be sold very frequently, can make it harder to generate forecasts. For example, an Internet-based footwear retailer may sell hundreds of different shoes, and for most days in a given time interval, there may be zero (or very few) sales of a particular type of shoe. Relatively few winter shoes may be sold for much of the summer months of a given year in this example scenario. On the other hand, when sales of such infrequently-sold items do pick up, they may be bursty—e.g., a lot of winter shoes may be sold in advance of, or during, a winter storm. The demand for some items may also be correlated with price reductions, holiday periods and other factors. Some traditional prediction approaches, when confronted with time series which consist largely of zero demand values, may be unable to predict non-zero demands with desired accuracy levels, especially for the large lead times which may sometimes be required to replenish the supplies of the items.
In today's competitive environment, the organizations responsible for stocking and selling such intermittent-demand items may be under substantial pressure to ensure that the supplies they maintain of various items are generally sufficient to meet customer needs. Sustained out-of-stock situations may, for example, lead to poor customer satisfaction and consequently to loss of customers. At the same time, the organizations also cannot afford to maintain excessive stocks of infrequently-purchased items—some of the organizations may for example sell millions of items, and the costs of overstocking all the items may quickly become unsustainable. Forecasting demand accurately for intermittently-needed items in a timely and efficient manner may thus present a non-trivial challenge.
While embodiments are described herein by way of example for several embodiments and illustrative drawings, those skilled in the art will recognize that embodiments are not limited to the embodiments or drawings described. It should be understood, that the drawings and detailed description thereto are not intended to limit embodiments to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope as defined by the appended claims. The headings used herein are for organizational purposes only and are not meant to be used to limit the scope of the description or the claims. As used throughout this application, the word “may” is used in a permissive sense (i.e., meaning having the potential to), rather than the mandatory sense (i.e., meaning must). Similarly, the words “include,” “including,” and “includes” mean including, but not limited to. When used in the claims, the term “or” is used as an inclusive or and not as an exclusive or. For example, the phrase “at least one of x, y, or z” means any one of x, y, and z, as well as any combination thereof.